Is it ok to send greeting message to a new subscriber?

That depends on your business model i would gess… i dont thinkg that there is a simple yes, or no, to this question 

I agree, this depends on business and for what that person is coming. But in general, I recommend giving free value first. By doing this, people are more likely to trust you and see you as the authority in your niche. Once you are authoritative (in their eyes) and they trust you, they are more likely to buy from you. And that’s when you upsell one of your paid products.

If you want more info on this, I recommend reading the book Marketing Made Simple by Donald Miller.

We do mostly use principles of Incoming marketing, but sending welcome DM to each new subsciber is a way of Direct marketing, I guess. And is it ok to use both ways? 

Or is it too “agressive” way DM lead magnets (we have a free introduction course) without “asking their permissions”?

I don’t see a problem sending a greeting message. If they just started to follow you, why not? It could lead to a new client. That is my thought. 

Using someone on your team, manually, or with a social seller, I don't see any problems. Yes, automating has problems, since the premise of automation is that the person interacts with the bot first, and not the other way around.

Hello,

I was wondering if it’s possible to send an automatic DM with Manychat to new subscriber to IG as I read that IG blocked this feature ?

I always DM new followers. Welcoming and thanking them. And I ask what interested them and brought them to the page. It’s a great convo starter. And I get a lot of bookings that way. To me it’s like you ignoring someone who physically walked into your brick and mortar establishment if you don’t say hi. 

@CBed did you get a reply to this?
This is exactly what I wanted to know and the reason I would use manychat
Thanks